The period of the function $f(x) = \frac{|\sin x| + |\cos x|}{|\sin x - \cos x|}$ is

The period of $\left(\tan \theta - \frac{1}{3} \tan^3 \theta\right) \left(\frac{1}{3} - \tan^2 \theta\right)^{-1}$,where $\tan^2 \theta \neq \frac{1}{3}$,is

Which of the following function$(s)$ is/are periodic?

The period of the function $f(x) = \log(\cos 2x) + \sin 4x$ is :-

Let $\alpha$ be the period of $3 \sin \frac{\pi x}{3} - \cos \frac{\pi x}{2} + \tan \frac{\pi x}{4}$,$\beta$ be the period of $\sin^2 \left( \frac{\pi}{7} + \frac{x}{4} \right) - \sin^2 \left( \frac{\pi}{7} - \frac{x}{4} \right)$,and $\gamma$ be the period of $\cos^4 x + \sin^4 x$. Then $\frac{\alpha \gamma}{\beta} = $

The period of the function $f(x) = e^{\log(\sin x)} + (\tan x)^3 - \operatorname{cosec}(3x - 5)$ is